Accessibility of Nilpotent Orbits in Classical Algebras

The work in this thesis provides a refinement in the classification of nilpotent orbits in classical algebras. Given an affine algebraic group and attached Lie algebra over an algebraically closed field k with good characteristic, we explore the relationship between the nilpotent orbits given by taking limits along cocharacters of the group. This can be used to determine the so-called accessibility order of the nilpotent orbits in the Lie algebra. In this thesis, the accessibility of nilpotent orbits in the general linear, symplectic and orthogonal algebras are completely determined, as well as possible differences that occur when k is no longer closed. Leaving the restriction of algebraic closure provides a topic for further research.